With betatron oscillation characteristics of the electron beam and ion channel effect taken into account,dispersion characteristics of electrostatic modes and TM modes for a relativistic electron beam guided by ion channel are studied.Dispersion relations are derived and solved numerically to investigate the dependence of the dispersion characteristics for electrostatic modes and TM modes on the betatron oscillation frequency and the ratio of the relativistic electron beam radius to the waveguide radius.The effects of the boundary current on the dispersion characteristic of the TM modes and the interaction between the betatron modes and TM modes are analyzed.When considering the boundary current,for a strong ion channel,a new low-frequency branch of the TM modes arises and the interaction frequency between the betatron modes and the TM01modes is increased with the same parameters.
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